With his players enjoying a scheduled day off from training on Wednesday, Southgate went for a 10-kilometre run and claims he was on course to beat his record time when he sustained the injury.
The 47-year-old tripped and tried to break the fall with his arm, only to end up dislocating his shoulder.
Southgate was punching the air in celebration 36 hours earlier as England beat Tunisia 2-1 but will have to tone things down if his side score a goal against Panama on Sunday.
“I might not be celebrating any goals as athletically in future!” he joked after being treated at a nearby hospital by England team doctor Rob Chakraverty, who was running with him.
“The doc has made it clear that punching the air is not an option.
“We have got such a great support team and they were there very quickly. They were supposed to be relaxing because we let the players have a bit of time off and I am causing them to work.
“We are lucky we have a top-class medical team around us, so it was fine. I had brilliant help from them, and I am just sorry that I managed to ruin their day off.”
Southgate returned to England’s base in time to hold a meeting with his players, who were taken aback when he arrived into the room with his arm in a sling.
“It is better this is me than one of the players,” he said.
“They were a bit surprised in the team meeting and were asking ‘what have you been doing!?’. As always, they were probably quite amused.
“It is good that we have had a quiet day today so I had prepared the meeting before and we are on to preparations for Panama.
“I am just a bit gutted because I was on for my record 10k time!”